Passive skyhook and groundhook damping vibration isolation system

ABSTRACT

A passive skyhook and groundhook damping vibration isolation system and a method for determining parameters thereof, which utilize the anti-resonance of an “inerter (b1, b2)-spring (k 1 , k 2 )-mass (m 1 , m 2 )” vibration state converting system to convert the resonance of the isolated mass into the resonance of the inerter, thus eliminating the resonance of the isolated mass, is provided. A damper spans and is connected in parallel to the inerter, preventing the damper from spanning and being connected in parallel to the isolated mass. The damper is not required to connect to an inertial reference frame, and the vibration of the isolated mass is suppressed.

FIELD OF TECHNOLOGY

The following relates the technical field of vibration attenuation andvibration isolation, particularly to a passive skyhook and groundhookdamping vibration isolation system.

BACKGROUND

Vibration isolation is a classical problem in the mechanicalengineering. Many machines, for example, cars, trains, heavy machinery,landing gears of airplanes, space landers, etc., require a vibrationisolation system. The purpose of vibration isolation is to reduce thetransmission of external disturbance to the sensitive parts of thesystem. A suspension, consisting of a spring and a damping element, mayreduce the response of the sensitive parts of the system to the externaldisturbance, thus achieving the purpose of vibration isolation.Isolation systems are usually designed to attenuate either shock orpersistent harmonic excitations.

People have been committed to the design and application research ofpassive vibration isolation systems for a long time. However,researchers have found that conventional passive vibration isolationsystems are unable to harmonize the conflict between the resonantresponse and the high-frequency attenuation, thus the furtherimprovement of the performance of the passive vibration isolationsystems is restricted. To solve this problem, Karnopp and Crosby haveproposed an ideal skyhook damping that can attenuate the resonantresponse without increasing the high-frequency transmissibility (D.Karnopp, M. J. Crosby, R. A. Harwood. “Vibration Control UsingSemi-Active Force Generators”, Journal of Engineering for Industry,96(2):6-9-626, 1974). A viscous damper in the vibration isolation systemof the ideal skyhook damping is required to be connected to an inertialreference frame. However, in many practical applications, it isimpossible that one end of a damper is connected to the isolated masswhile the other end thereof is connected to an inertial reference frame.A vehicle suspension system is an obvious example. FIG. 1 shows asimplified ideal-skyhook damping vehicle suspension system. FIG. 2 showsan equivalent mechanical network of FIG. 1. One terminal of the isolatedmass m₂ is the center of mass, while the other terminal thereof is afixed point in the inertial reference frame. For a system standing stillrelative to the inertial reference frame, the inertial reference framebecomes a common end of the damper c_(sky) and the isolated mass m₂.Therefore, the damper c_(sky) may span and be connected in parallel tothe isolated mass m₂ via the inertial reference frame to absorb thevibration energy of the mass m₂ and to suppress the resonance of themass m₂. However, for a system moving relative to the inertial referenceframe, for example, a vehicle suspension, the damper c_(sky) is unableto span the isolated mass m₂ without the inertial reference frame as anatural common end. This is the root cause why people think that anideal skyhook damping cannot be realized passively.

To achieve the vibration isolation effect of the ideal skyhook damping,a replaceable implementation way is employed to realize the skyhookdamping, including active and semi-active implementation ways. In theactive implementation way, a sensor, an actuator and electronic controltechnology are employed to realize the skyhook damping (C. R. Fuller, S.J. Elliott, P. A. Nelson. “Active Control of Vibration”, Academic Press,New York,1996). In the semi-active implementation way, anelectronically-controlled damping adjustment method is employed torealize the skyhook damping (S. Rakheja, “Vibration and Shock IsolationPerformance of a Semi-Active ‘on-off’ Damper”, Journal of Vibration,Acoustics, Stress, and Reliability in Design, 107(4):398-403, 1985).Although the active and semi-active implementation ways can generate theexpected effects in theory, the active and semi-active vibrationisolation systems require external energy input, and have complexstructure and poorer reliability than a passive vibration isolationsystem. Furthermore, during the vibration isolation, both an activevibration isolation system and a semi-active vibration isolation systemwill have three links, including the measurement by a sensor, thecalculation by a controller and the execution by an actuation mechanism.There are many intermediate links. Furthermore, the errors and time-lagof the measurement by the sensor, the calculation by the controller andthe actuation mechanism seriously affect the real-time performance andeffectiveness of control, thus making the actual vibration isolationeffect of the active and semi-active vibration isolation systemsdifficult to reach the expected effect in theory.

U.S. Pat. No. 6,315,094B1 disclosed a passive skyhook vibrationisolation system, comprising a main vibration system and a dynamicvibration absorber with damping. In the main vibration system, a springand a damper support a main mass. The dynamic vibration absorber withdamping is attached onto the main mass of the main vibration system. Thevibration of the main mass is suppressed by adjusting the parameters ofthe dynamic vibration absorber. In such a passive skyhook vibrationisolation system, there is an irreconcilable conflict between the massof the vibrator of the vibration absorber and the amplitude of thevibrator. According to the principle that the natural frequency of thevibration absorber is the same to that of the main vibration system, onone hand, if the amplitude of the vibrator is to be reduced, thestiffness of the spring of the vibration absorber is to be enhanced, andthe mass of the vibrator is to be increased correspondingly. As aresult, the mass attached onto the main mass will be increasedcertainly. Taking a car suspension system as example, the mass attachedonto the car body will be 69 kg even though the minimum percentage ofthe mass of the vibrator to the main mass in this patent is 5%, giventhe mass of the car body is 1380 kg. Apparently, the kerb mass of thecar increases. On the other hand, if the mass of the vibrator is to bereduced, the stiffness of the spring of the vibration absorber is to bereduced, thus the amplitude of the vibrator increases. Apparently, it isdisadvantageous to the arrangement of the vibration absorber.

In conclusion, it may be found that there is an urgent demand for apassive skyhook and groundhook damping vibration isolation system, inorder to overcome the shortcomings of the need of external energy input,complex structure, and poor reliability and real-time performance inactive and semi-active implementation methods, simultaneously avoidingthe problem of the conflict between the mass of a vibrator and theamplitude of the vibrator when a dynamic vibration absorber with dampingis applied, harmonize the conflict between the resonant response and thehigh-frequency attenuation, and to suppress the resonance of theisolated mass without increasing the high-frequency transmissibility.

SUMMARY

The present invention provides a passive skyhook and groundhook dampingvibration isolation system, which can overcome the shortcomings in theabove implementation methods and can achieve a vibration isolationeffect close to that of the ideal skyhook and groundhook damping.

The present invention employs an inerter (also referred to as inertialmass accumulator or inertial accumulator, referring to U.S. Pat. No.7,316,303B2, No. 20090108510A1 and No. 20090139225A1) as a primaryelement of the system.

The inertial mass accumulation suspensions disclosed in Chinese PatentsNo. 201010281331.9, No. 201010281336.1 and No. 201010281307.5 areemployed basically to reduce the vertical acceleration of a vehicle bodyand the dynamic load of tires, improve ride comfort of the vehicleand-tire grip, and to harmonize the conflict between ride comfort andtire grip. However, the above patents had not yet provided any specificsuspension parameters having a decisive impact on the performance of thesuspensions or any relations between the parameters, nor a method fordetermining these parameters. To realize the functions of the idealskyhook and groundhook damping passively, the present inventiondiscloses not only a passive skyhook and groundhook damping vibrationisolation system, but also a method for determining the parameters ofthis system.

The technical problem to be solved by the present invention is toprovide a passive skyhook and groundhook damping vibration isolationsystem, in order to overcome the technical shortcomings of the need ofexternal energy input, complex structure, and poor reliability andreal-time performance in active and semi-active implementation methods,and to solve the technical problem that the damper in an ideal skyhookand groundhook damping vibration isolation system is required to beconnected to an inertial reference frame. The passive skyhook andgroundhook damping vibration isolation system does not require thedamper to connect to an inertial reference frame, maximizes the idealskyhook and groundhook damping, and suppresses the vibration of theisolated mass.

The following technical solutions are employed by the present invention:the anti-resonance of an “inerter-spring-mass” vibration stateconverting system is utilized to convert the resonance of the isolatedmass into the resonance of the inerter, thus eliminating the resonanceof the isolated mass. On this base, a damper spans and is connected inparallel to the inerter, thus preventing the damper from spanning andbeing connected in parallel to the isolated mass, and overcoming thetechnical bias that the damper in ideal skyhook and groundhook dampingvibration isolation system is required to be connected to an inertialreference frame.

The passive skyhook and groundhook damping vibration isolation systemdisclosed by the present invention is a system with two degrees offreedom (2DOF), comprising a “spring k-damper c” parallel body, a“spring k_(t)-damper c_(t)” parallel body, a skyhook damper c_(sky), agroundhook damper c_(gnd), a moving foundation, a mass m₁ vibrationstate converting system and a mass m₂ vibration state converting system.

The “spring k_(t)-damper c_(t)” parallel body consists of a spring k_(t)and a damper c_(t) connected in parallel; the mass m₁ vibration stateconverting system comprises a mass m₁ and a mass m₁ vibration stateconverter, the mass m₁ vibration state converter consisting of a springk₁ and an inerter b₁ connected in parallel, the mass m₁ vibration stateconverter being connected in series to and supporting the mass m₁; the“spring k_(t)-damper c_(t)” parallel body is connected in series to themass m₁ vibration state converter and supports the whole mass m₁vibration state converting system via the mass m₁ vibration stateconverter; the moving foundation is connected in series to and supportsthe “spring k_(t)-damper c_(t)” parallel body; the groundhook damperc_(gnd) is connected in parallel to the mass m₁ vibration stateconverter to form the parallel body of the mass m₁ vibration stateconverter and the groundhook damper c_(gnd).

The “spring k-damper c” parallel body consists of a spring k and adamper c connected in parallel; the mass m₂ vibration state convertingsystem comprises a mass m₂ and a mass m₂ vibration state converter, themass m₂ vibration state converter consisting of a spring k₂ and aninerter b₂ connected in parallel, the mass m₂ vibration state converterbeing connected in series to and supporting the mass m₂; the “springk-damper c” parallel body is connected in series to the mass m₂vibration state converter, and supports the whole mass m₂ vibrationstate converting system via the mass m₂ vibration state converter; themass m₁ is connected in series to and supports the “spring k-damper c”parallel body; the skyhook damper c_(sky) is connected in parallel tothe mass m₂ vibration state converter to from the parallel body of themass m₂ vibration state converter and the skyhook damper c_(sky).

In the present invention, the parallel body of the mass m₁ vibrationstate converter and the skyhook damper c_(gnd) in the 2DOF passiveskyhook and groundhook damping vibration isolation system is omitted,and two ends of the “spring k_(t)-damper c_(t)” parallel body aredirectly connected in series to the mass m₁ and the moving foundation,respectively, to form a 2DOF passive skyhook damping vibration isolationsystem.

In the present invention, the parallel body of the mass m₂ vibrationstate converter and the skyhook damper c_(sky) in the 2DOF passiveskyhook and groundhook damping vibration isolation system is omitted,and two ends of the “spring k-damper c” parallel body are directlyconnected in series to the mass m₁ and the mass m₂, respectively, toform a 2DOF passive groundhook damping vibration isolation system.

In the present invention, the “spring k_(t)-damper c_(t)” parallel body,the parallel body of the mass m₁ vibration state converter and theskyhook damper c_(gnd) and the mass m₁ in the 2DOF passive skyhook andgroundhook damping vibration isolation system are omitted, and the“spring k-damper c” parallel body is directly connected in series to themoving foundation to form an SDOF (Single Degree of Freedom) passiveskyhook damping vibration isolation system.

In the 2DOF passive skyhook and groundhook damping vibration isolationsystem disclosed by the present invention, the mass of the mass m₂ ism₂, the stiffness of the spring k₂ is k₂, the inerterance of the inerterb₂ is b₂, the damping of the skyhook damper c_(sky) is c_(sky), thestiffness of the spring k is k, the damping of the damper c is c; themass of the mass m₁ is m₁, the stiffness of the spring k₁ is k₁, theinerterance of the inerter b₁ is b₁, the damping of the groundhookdamper c_(gnd) is c_(gnd), the stiffness of the spring k_(t) is k_(t),and the damping of the damper c_(t) is c_(t).

A method for determining parameters k₁, b₁, k₂ and b₂ of the 2DOFpassive skyhook and groundhook damping vibration isolation systemincludes the following steps.

Step 1: The skyhook damper c_(sky) and the groundhook damper c_(gnd) inthe 2DOF passive skyhook and groundhook damping vibration isolationsystem are omitted to obtain a conventional 2DOF passive vibrationisolation system; the known parameters of the conventional 2DOF passivevibration isolation system are as follows: the mass of the mass m₂ ism₂, the stiffness of the spring k is k, the damping of the damper c isc, the mass of the mass m₁ is m₁, the stiffness of the spring k_(t) isk_(t), and the damping of the damper c_(t) is c_(t); and the resonancefrequency ω₂ of the mass m₂ in the conventional 2DOF passive vibrationisolation system is calculated according to the following equation:ω₂=√{square root over (k/m ₂)}.

Step 2: The anti-resonance frequency ω_(2A) of the mass m₂ vibrationstate converting system is calculated according to the followingequation:ω_(2A)=√{square root over (k ₂ /b ₂)}.

Step 3: A relational expression of k₂ and b₂ is determined according tothe principle that ω_(2A) is approximately equal to ω₂:k/m ₂ =k ₂ /b ₂,

where, k and m are known parameters, and k₂ and b₂ are parameters to bedetermined.

Step 4: The resonance frequency ω₁ of the mass m₁ in the conventional2DOF passive vibration isolation system is calculated according to thefollowing equation:ω₁=√{square root over ((k ₁ +k)/m ₁)}.

Step 5: The anti-resonance frequency ω_(1A) of the mass m₁ vibrationstate converting system is calculated according to the followingequation:ω_(1A)=√{square root over (k ₁ /b ₁)}.

Step 6: A relational expression of k₁ and b₁ is determined according tothe principle that ω_(1A) is approximately equal to ω₁:(k _(t) +k)/m ₁ =k ₁ /b ₁,

where, k_(t), k and m₁ are known parameters, and k₁ and b₁ areparameters to be determined.

Step 7: The values of parameters k₁ and k₂ are determined. Calculationsand tests show that the performance of the passive skyhook andgroundhook damping vibration isolation system disclosed by the presentinvention will be closer to that of an ideal skyhook and groundhookdamping vibration isolation system if the values of k₁ and k₂ aresmaller. However, too small values of k₁ and k₂ will result in a toolarge relative stroke between the mass m₁ and the mass m₂ and betweenthe mass m₁ and the moving foundation. To avoid a too large relativestroke, k₁ should be greater than or equal to k_(t)/3, and k₂ should begreater than or equal to k/3. Meanwhile, the values of k₁ and k₂ cannotbe too large. Too large values of k₁ and k₂ will deteriorate theperformance of the passive skyhook and groundhook damping vibrationisolation system. Calculations and tests show that the performance ofthe passive skyhook and groundhook damping vibration isolation systemdisclosed by the present invention can be close to that of an idealskyhook and groundhook damping vibration isolation system when k₁ isless than or equal to k_(t) and k₂ is less than or equal to k.Therefore, in the case of k_(t)/3≦k₁≦k_(t) and k/3≦k₂≦k, that is, k₁ iswithin [k_(t)/3, k_(t)] and k₂ is within [k/3, k], the passive skyhookand groundhook damping vibration isolation system can achieve the effectrequired by the present invention.

Step 8: The known parameters of the ideal 2DOF skyhook and groundhookdamping vibration isolation system are as follows: the mass of the massm₁ is m₁, the mass of the mass m₂ is m₂, the stiffness of the spring kis k, the damping of the damper c is c, the stiffness of the springk_(t) is k_(t), the damping of the damper c_(t) is c_(t), the damping ofthe skyhook damper c_(sky) is c_(sky), and the damping of the groundhookdamper c_(gnd) is c_(gnd). The values of k₁ and k₂ are selected from theranges determined in Step 7, the specific values of parameters b₁ and b₂are determined finally according to the relation of k₂ and b₂ determinedin Step 3 and the relation of k₁ and b₁ determined in Step 6:

${b_{1} = {\frac{k_{1}}{\left( {k_{i} + k} \right)}m_{i}}},{b_{2} = {\frac{k_{2}}{k}{m_{2}.}}}$

With respect to the skyhook damping vibration isolation systems usingactive and semi-active implementation methods, the present invention issimple and reliable and requires no energy input; with respect to thepassive skyhook damping vibration isolation systems using dynamiticvibration absorbers with damping, the present invention avoids theproblem on the conflict between the mass of a vibrator and the amplitudeof the vibrator; and, with respect to conventional passive vibrationisolation systems, the performance of the vibration isolation systemdisclosed by the present invention is improved significantly.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an ideal skyhook damping vehiclesuspension system;

FIG. 2 is a schematic diagram of an equivalent mechanical network of anideal skyhook damping vehicle suspension system;

FIG. 3 is a schematic diagram of a mass m₂ vibration state convertingsystem;

FIG. 4 is a schematic diagram of an ideal 2DOF skyhook and groundhookdamping vibration isolation system;

FIG. 5 is a schematic diagram of a 2DOF passive skyhook and groundhookdamping vibration isolation system;

FIG. 6 is a schematic diagram of a conventional 2DOF passive vibrationisolation system;

FIG. 7 is a schematic diagram of a mass m₁ vibration state convertingsystem;

FIG. 8 is a graphical diagram of the displacement transmissibility of amass m₂ in the 2DOF passive skyhook and groundhook damping vibrationisolation system;

FIG. 9 is a graphical diagram of the displacement transmissibility of amass m₁ in the 2DOF passive skyhook and groundhook damping vibrationisolation system;

FIG. 10 is a schematic diagram of specific implementation way 1 of the2DOF passive skyhook and groundhook damping vibration isolation system;

FIG. 11 is a schematic diagram of specific implementation way 2 of the2DOF passive skyhook and groundhook damping vibration isolation system;

FIG. 12 is a schematic diagram of specific implementation way 3 of the2DOF passive skyhook and groundhook damping vibration isolation system;

FIG. 13 is a schematic diagram of a 2DOF passive skyhook dampingvibration isolation system;

FIG. 14 is a graphical diagram of the displacement transmissibility of amass m₂ in the 2DOF passive skyhook damping vibration isolation system;

FIG. 15 is a schematic diagram of a 2DOF passive groundhook dampingvibration isolation system;

FIG. 16 is a graphical diagram of the displacement transmissibility of amass m₁ in the 2DOF passive groundhook damping vibration isolationsystem; and

FIG. 17 is a schematic diagram of an SDOF passive skyhook dampingvibration isolation system.

In the figures: 1—Mass m₂; 2—Spring k₂; 3—Inerter b₂; 4—Skyhook damperc_(sky); 5—Spring k; 6—Damper c; 7—Groundhook damper c_(gnd); 8—Mass m₁;9—Spring k_(t); 10—Damper c_(t); 11—Moving foundation; 12—Spring k₁;13—Inerter b₁; 14—Lever L₂; 15—Lever L₁; 16—Fixed rod R₂; 17—Fixed rodR₁; 18—Slideway; 19—Torsion spring A; 20—Torsion damper A; 21—Torsionspring B; 22—Torsion damper B; 23—Skyhook damping pillar; 24—Groundhookdamping pillar; 25—Flywheel chamber A; 26—Flywheel A; 27—Screw supportA; 28—Nut A; 29—Screw A; 30—Stroke chamber A; 31—Viscous oil;32—Cylinder A; 33—Piston A with a damping hole; 34—Oil; 35—Piston rod A;36—Flywheel chamber B; 37—Flywheel B; 38—Screw support B; 39—Nut B;40—Screw B; 41—Stroke chamber B; 42—Cylinder B; 43—Piston B with adamping hole; 44—Piston rod B; 45—Mass m₂ vibration state converter;46—Mass m₂ vibration state converting system; 47—Mass m₁ vibration stateconverter, 48—Mass m₁ vibration state converting system.

DETAILED DESCRIPTION

As shown in FIG. 3, a mass m₂ vibration state converter 45 consists of aspring k₂ 2 and an inerter b₂ 3 connected in parallel. The mass m₂vibration state converter 45 is connected in series to and supports amass m₂ 1, thus, a mass m₂ vibration state converting system forms. As asimple system, the movement of the mass m₂ vibration state convertingsystem may be described by the following second-order differentialequation:m ₂ {umlaut over (z)} ₂ +b ₂({umlaut over (z)} ₂ −{umlaut over (z)}_(r2))+k ₂(z ₂ −z _(r2))=0,

where, z₂ is the displacement of the mass m₂ 1, z_(r2) is thedisplacement input of the system, k₂ and b₂ are the stiffness of thespring k₂ 2 and the interance of the inerter b₂ 3.

Laplace conversion is performed to the above equation to obtain thefollowing equation:

${\frac{Z_{2}(s)}{Z_{t\; 2}(s)} = \frac{\left( {{b_{2}s^{2}} + k_{2}} \right)}{{\left( {m_{2} + b_{2}} \right)s^{2}} + k_{2}}},$

supposed that s=jω, the ratio of amplitudes of z₂ and z_(r2) may beobtained according to the above equation, so that the displacementtransmissibility of the system is as follows:

${T({j\omega})} = {{\frac{Z_{2}({j\omega})}{Z_{r\; 2}({j\omega})}} = {{\frac{{{- b_{2}}\omega^{2}} + k_{2}}{{{- \left( {m_{2} + b_{2}} \right)}\omega^{2}} + k_{2}}}.}}$In the case of T(jω)=0, the system will have anti-resonance and theanti-resonance frequency ω_(2A) is √{square root over (k₂/b₂)}. At thismoment, the amplitude of the mass m₂ 1 is 0, while the inerter b₂ 3 isin a resonant state. Therefore, when the mass m₂ 1 is in a resonantstate in a certain system A, the mass m₂ 1 in the system A is replacedwith the mass m₂ vibration state converting system 46, and theanti-resonance frequency ω_(2A) is made close to the resonance frequencyof the mass m₂ 1 in the system A. Thus, the resonance of the mass m₂ 1may be converted into the resonance of the inerter b₂ 3 so as toeliminate the resonance of the mass m₂ 1, thereby providing a solutionfor the passive implementation of the ideal skyhook and groundhookdamping.

As shown in FIG. 4, an ideal 2DOF (Two Degrees of Freedom) skyhook andgroundhook damping vibration isolation system comprises a mass m₁ 8 anda mass m₂ 1, a “spring k 5-damper c 6” parallel body, a “spring k_(t)9-damper c_(t) 10” parallel body, a skyhook damper c_(sky) 4 and agroundhook damper c_(gnd) 7. Wherein, the “spring k 5-damper c 6”parallel body consists of a spring k 5 and a damper c 6 connected inparallel. The “spring k_(t) 9-damper c_(t) 10” parallel body consists ofa spring k_(t) 9 and a damper c_(t) 10 connected in parallel. One end ofthe “spring k 5-damper c 6” parallel body is connected in series to themass m₂ 1, while the other end thereof is connected in series to themass m₁ 8. The mass m₁ 8 supports the mass m₂ 1 via the “spring k5-damper c 6” parallel body. One end of the “spring k_(t) 9-damper c_(t)10” parallel body is connected in series to the mass m₁ 8, while theother end thereof is connected in series to a moving foundation 11. Themoving foundation 11 supports the mass m₁ 8 via the “spring k_(t)9-damper c_(t) 10” parallel body. One ends of the skyhook damper c_(sky)4 and the groundhook damper c_(gnd) 7 are connected to the mass m₂ 1 andthe mass m₁ 8, respectively, while the other ends thereof are connectedto an inertial reference frame.

As shown in FIG. 5, as a passive implementation system of the ideal 2DOFskyhook and groundhook damping vibration isolation system, a 2DOFpassive skyhook and groundhook damping vibration isolation systemcomprises a “spring k 5-damper c 6” parallel body, a “spring k_(t)9-damper c_(t) 10” parallel body, a skyhook damper c_(sky) 4, agroundhook damper C_(gnd) 7, a moving foundation 11, a mass m₁ vibrationstate converting system 48 and a mass m₂ vibration state convertingsystem 46.

The “spring k_(t) 9-damper c_(t) 10” parallel body consists of a springk_(t) 9 and a damper c_(t) 10 connected in parallel. The mass m₁vibration state converting system 48 comprises a mass m₁ 8 and a mass m₁vibration state converter 47. The mass m₁ vibration state converter 47consists of a spring k₁ 12 and an inerter b₁ 13 connected in parallel.The mass m₁ vibration state converter 47 is connected in series to andsupports the mass m₁ 8. The “spring k_(t) 9-damper c_(t) 10” parallelbody is connected in series to the mass m₁ vibration state converter 47and supports the whole mass m₁ vibration state converting system 48 viathe mass m₁ vibration state converter 47. The moving foundation 11 isconnected in series to and supports the “spring k_(t) 9-damper c_(t) 10”parallel body. The groundhook damper c_(gnd) 7 is connected in parallelto the mass m₁ vibration state converter 47 to form the parallel body ofthe mass m₁ vibration state converter 47 and the groundhook damperc_(gnd) 7.

The “spring k 5-damper c 6” parallel body consists of a spring k 5 and adamper c 6 connected in parallel. The mass m₂ vibration state convertingsystem 46 comprises a mass m₂ 1 and a mass m₂ vibration state converter45. The mass m₂ vibration state converter 45 consists of a spring k₂ 2and an inerter b₂ 3 connected in parallel. The mass m₂ vibration stateconverter 45 is connected in series to and supports the mass m₂ 1. The“spring k 5-damper c 6” parallel body is connected in series to the massm₂ vibration state converter 45, and supports the whole mass m₂vibration state converting system 46 via the mass m₂ vibration stateconverter 45. The mass m₁ is connected in series to and supports the“spring k 5-damper c 6” parallel body. The skyhook damper c_(sky) 4 isconnected in parallel to the mass m₂ vibration state converter 45 tofrom the parallel body of the mass m₂ vibration state converter 45 andthe skyhook damper c_(sky) 4.

In the 2DOF passive skyhook and groundhook damping vibration isolationsystem, the parallel body of the mass m₁ vibration state converter 47and the groundhook damper c_(gnd) 7 and the “spring k_(t) 9-damper c_(t)10” parallel body are exchanged in position with each other, and theparallel body of the mass m₂ vibration state converter 45 and theskyhook damper c_(sky) 4 and the “spring k 5-damper c 6” parallel bodyare exchanged in position with each other. The inerter b₂ 3 and theinerter b₁ 13 may be one of a rack and pinion inerter (referring to U.S.Pat. No. 6,315,094B1), a ballscrew inerter (referring to U.S.Publication No. 2009/0108510A1) and a hydraulic inerter (referring toU.S. Publication No. 2009/0139225A1).

In the 2DOF passive skyhook and groundhook damping vibration isolationsystem disclosed by the present invention, the mass of the mass m₂ 1 ism₂, the stiffness of the spring k₂ 2 is k₂, the inerterance of theinerter b₂ 3 is b₂, the damping of the skyhook damper c_(sky) 4 isc_(sky), the stiffness of the spring k 5 is k, the damping of the damperc 6 is c, the mass of the mass m₁ 8 is m₁, the stiffness of the springk₁ 12 is k₁, the inerterance of the inerter b₁ 13 is b₁, the damping ofthe groundhook damper c_(gnd) 7 is c_(gnd), the stiffness of the springk_(t) 9 is k_(t), and the damping of the damper c_(t) 10 is c_(t).

A method for determining parameters k₁, b₁, k₂ and b₂ of the 2DOFpassive skyhook and groundhook damping vibration isolation systemcomprises the following steps.

Step 1: In FIG. 4, the skyhook damper c_(sky) 4 and the groundhookdamper c_(gnd) 7 in the ideal 2DOF skyhook and groundhook dampingvibration isolation system are omitted to obtain a conventional 2DOFpassive vibration isolation system, as shown in FIG. 6; the knownparameters of the conventional 2DOF passive vibration isolation systemare as follows: the mass of the mass m₂ 1 is m₂, the stiffness of thespring k 5 is k, the damping of the damper c 6 is c, the mass of themass m₁ 8 is m₁, the stiffness of the spring k_(t) 9 is k_(t), and thedamping of the damper c_(t) 10 is c_(t); and the resonance frequency ω₂of the mass m₂ 1 in the conventional 2DOF passive vibration isolationsystem is calculated according to the following equation:ω₂=√{square root over (k/m ₂)}.

Step 2: As shown in FIG. 3, the anti-resonance frequency ω_(2A) of themass m₂ vibration state converting system 46 is calculated according tothe following equation:ω_(2A)=√{square root over (k ₂ /b ₂)}.

Step 3: A relational expression of k₂ and b₂ is determined according tothe principle that ω_(2A) is approximately equal to ω₂:k/m ₂ =k ₂ /b ₂,

where, k and m are known parameters, and k₂ and b₂ are parameters to bedetermined.

Step 4: The resonance frequency ω₁ of the mass m₁ 8 in the conventional2DOF passive vibration isolation system is calculated according to thefollowing equation:ω₁=√{square root over ((k _(t) +k)/m ₁)}.

Step 5: As shown in FIG. 7, the anti-resonance frequency ω_(1A) of themass m₁ vibration state converting system 48 is calculated according tothe following equation:ω_(1A)=√{square root over (k ₁ /b ₁)}.

Step 6: A relational expression of k₁ and b₁ is determined according tothe principle that ω_(1A) is approximately equal to ω₁:(k _(t) +k)/m ₁ =k ₁ /b ₁,

where, k_(t), k and m₁ are known parameters, and k₁ and b₁ areparameters to be determined.

Step 7: The values of parameters k₁ and k₂ are determined. Calculationsand tests show that the performance of the passive skyhook andgroundhook damping vibration isolation system disclosed by the presentinvention will be closer to that of an ideal skyhook and groundhookdamping vibration isolation system if the values of k₁ and k₂ aresmaller. However, too small values of k₁ and k₂ will result in a toolarge relative stroke between the mass m₁ 8 and the mass m₂ 1 andbetween the mass m₁ 8 and the moving foundation 11. To avoid a too largerelative stroke, k₁ should be greater than or equal to k/3, and k₂should be greater than or equal to k/3. Meanwhile, the values of k₁ andk₂ cannot be too large. Too large values of k₁ and k₂ will deterioratethe performance of the passive skyhook and groundhook damping vibrationisolation system. Calculations and tests show that the performance ofthe passive skyhook and groundhook damping vibration isolation systemdisclosed by the present invention can be close to that of an idealskyhook and groundhook damping vibration isolation system when k₁ isless than or equal to k₁ and k₂ is less than or equal to k. Therefore,in the case of k_(t)/3≦k₁≦k_(t) and k/3≦k₂≦k, that is, k₁ is within[k_(t)/3, k_(t)] and k₂ is within [k/3, k], the passive skyhook andgroundhook damping vibration isolation system can achieve the effectsrequired by the present invention.

Step 8: The known parameters of the ideal 2DOF skyhook and groundhookdamping vibration isolation system are as follows: the mass of the massm₁ 8 is m₁, the mass of the mass m₂ 1 is m₂, the stiffness of the springk 5 is k, the damping of the damper c 6 is c, the stiffness of thespring k_(t) 9 is k_(t), the damping of the damper c_(t) 10 is c_(t),the damping of the skyhook damper c_(sky) 4 is c_(sky), and the dampingof the groundhook damper c_(gnd) 7 is c_(gnd). The values of k₁ and k₂are selected from the ranges determined in Step 7, the specific valuesof parameters b₁ and b₂ are determined finally according to the relationof k₂ and b₂ determined in Step 3 and the relation of k₁ and b₁determined in Step 6:

${b_{i} = {\frac{k_{1}}{\left( {k_{1} + k} \right)}m_{1}}},{b_{2} = {\frac{k_{2}}{k}{m_{2}.}}}$

For example, the known parameters of the conventional passive vibrationisolation system are as follows: m₂=317.5 kg, k=22000N/m, c=1500N·s/m,m₁=45.4 kg, k_(t)=192000N/m, and c_(t)=0; the known parameters of theideal skyhook and groundhook damping vibration isolation system are asfollows: c_(sky)=2800N·s/m, c_(gnd)=3200N·s/m, and the other parametersare the same to those of the conventional passive vibration isolationsystem; and, in the passive skyhook and groundhook damping vibrationisolation system, there are four parameters to be determined, includingk₁, b₁, k₂ and b₂, and the other parameters all are known parameters andthe same to those of the conventional passive vibration isolationsystem.

In this example, the method for determining parameters k₁, b₁, k₂ and b₂of the 2DOF passive skyhook and groundhook damping vibration isolationsystem comprises the following steps:

Step 1: The resonance frequency ω₂ of the mass m₂ 1 in the conventional2DOF passive vibration isolation system is calculated according to thefollowing equation:ω₂=√{square root over (k/m ₂)}=√{square root over (22000/317.5)}.

Step 2: The anti-resonance frequency ω_(2A) of the mass m₂ vibrationstate converting system 46 is calculated according to the followingequation:ω_(2A)=√{square root over (k ₂ /b ₂)}.

Step 3: A relational expression of k₂ and b₂ is determined according tothe principle that ω_(2A) is approximately equal to ω₂:22000/317.5=k ₂ /b ₂.

Step 4: The resonance frequency ω₁ of the mass m₁ 8 in the conventional2DOF passive vibration isolation system is calculated according to thefollowing equation:ω₁=√{square root over ((k _(t) +k)/m ₁)}=√{square root over((192000+22000)/45.4)}=√{square root over (214000/45.4)}.

Step 5: The anti-resonance frequency ω_(1A) of the mass m₁ vibrationstate converting system 48 is calculated according to the followingequation:ω_(1A)=√{square root over (k ₁ /b ₁)}.

Step 6: A relational expression of k₁ and b₁ is determined according tothe principle that ω_(1A) is approximately equal to ω₁:214000/45.4=k ₁ /b ₁.

Step 7: The values of parameters k₁ and k₂ are determined. To avoid atoo large relative stroke and to ensure that the performance of thepassive skyhook and groundhook damping vibration isolation system willnot be deteriorated, k₁ and k₂ should be selected from [k_(t)/3, k_(t)]and [k/3, k], respectively, that is, from [64000, 192000] and [7333,22000], respectively. Here, k₁=192000N/m, and k₂=15000N/m.

Step 8: The specific values of parameters b₁ and b₂ are determinedfinally according to the relation of k₂ and b₂ determined in Step 3 andthe relation of k₁ and b₁ determined in Step 6:

${b_{1} = {{\frac{k_{1}}{\left( {k_{1} + k} \right)}m_{1}} = {{\frac{192000}{214000} \times 45.4} = 40.7}}},{b_{2} = {{\frac{k_{2}}{k}m_{2}} = {{\frac{15000}{22000} \times 317.5} = {216.5.}}}}$

After the parameters k₁, b₁, k₂ and b₂ are determined, all parameters ofthe passive skyhook and groundhook damping vibration isolation systemare obtained, including m₂=317.5 kg, k=22000N/m, c=1500N·s/m, m₁=45.4kg, k_(t)=192000N/m, c_(t)=0, c_(sky)=2800N·s/m, c_(gnd)=3200N·s/m,k₁=192000N/m, k₂=15000N/m, b₁=40.7 kg, and b₂=216.5 kg.

After all parameters of the passive skyhook and groundhook dampingvibration isolation system are determined by the above method, the idealskyhook and groundhook damping vibration isolation system is realizedpassively, so that the damper is not required any more to be connectedto an inertial reference frame. As a result, the technical bias that thedamper in the ideal skyhook and groundhook damping vibration isolationsystem is required to be connected to an inertial reference frame isovercomed.

As shown in FIG. 8, on the curve of the displacement transmissibility ofthe mass m₂, there are two peaks in the conventional passive vibrationisolation system. The two peaks are resulted from the resonance of themass m₂ and mass m₁ at an inherent frequency, and the frequencies are1.2 Hz and 10.2 Hz, respectively. Compared with the conventional passivevibration isolation system, the ideal skyhook and groundhook dampingvibration isolation system and the passive skyhook and groundhookdamping vibration isolation system have numerical values at 1.2 Hzdecreased by 68.1% and 60%, respectively, and numerical values at 10.2Hz decreased by 62.3% and 58%, respectively.

As shown in FIG. 9, on the curve of the displacement transmissibility ofthe mass m₁, there is a big peak in the conventional passive vibrationisolation system. The peak is resulted from the resonance of mass m₁ atan inherent frequency, and the frequency is 10.2 Hz. Compared with theconventional passive vibration isolation system, the ideal skyhook andgroundhook damping vibration isolation system and the passive skyhookand groundhook damping vibration isolation system have numerical valuesat this frequency decreased by 69.1% and 65.4%, respectively.

From the curves in FIG. 8 and FIG. 9 and the above analysis, it can befound that the ideal skyhook and groundhook damping vibration isolationsystem can suppress the resonance of the mass m₂ and mass m₁ completely,and the passive skyhook and groundhook damping vibration isolationsystem can suppress the resonance of the mass m₂ and mass m₁ well. Thedisplacement transmissibility of the passive skyhook and groundhookdamping vibration isolation system is close to that of the ideal skyhookand groundhook damping vibration isolation system. The vibrationisolation performance of the two systems is superior to that of theconventional passive vibration isolation system apparently.

FIG. 10 shows the specific implementation way 1 of the 2DOF passiveskyhook and groundhook damping vibration isolation system. The systemcomprises a mass m₁ 8 and a mass m₂ 1, a “spring k 5-damper c 6”parallel body, a “spring k_(t) 9-damper c_(t) 10” parallel body, a“spring k₁ 12-inerter b₁ 13” parallel body, a “spring k₂ 2-inerter b₂ 3”parallel body, a skyhook damper c_(sky) 4, a groundhook damper c_(gnd)7, a moving foundation 11, a lever L₁ 15 and a lever L₂ 14, a fixed rodR₁ 17 and a fixed rod R₂ 16, and a slideway 18. The “spring k 5-damper c6” parallel body consists of a spring k 5 and a damper c 6 connected inparallel. The “spring k_(t) 9-damper c_(t) 10” parallel body consists ofa spring k_(t) 9 and a damper c_(t) 10 connected in parallel. The“spring k₁ 12-inerter b₁ 13” parallel body consists of a spring k₁ 12and an inerter b₁ 13 connected in parallel. The “spring k₂ 2-inerter b₂3” parallel body consists of a spring k₂ 2 and an inerter b₂ 3 connectedin parallel. The mass m₂ 1, the mass m₁ 8 and the moving foundation 11are supported on the vertical slideway 18 in a rolling way to slide upand down along the vertical slideway 18. The fulcrum of the lever L₂ 14is fixed on the mass m₂ 1. The upper end of the “spring k 5-damper c 6”parallel body is hinged to one end of the lever L₂ 14, while the lowerend thereof is hinged to the mass m₁ 8. The upper end of the “spring k₂2-inerter b₂ 3” parallel body is hinged to the other end of the lever L₂14, while the lower end thereof is hinged to one end of the fixed rod R₂16. The other end of the fixed rod R₂ 16 is fixed on the mass m₂ 1. Thefulcrum of the lever L₁ 15 is fixed on the mass m₁ 8, the upper end ofthe “spring k_(t) 9-damper c_(t) 10” parallel body is hinged to one endof the lever L₁ 15, while the lower end thereof is hinged to the movingfoundation 11. The upper end of the “spring k₁ 12-inerter b₁ 13”parallel body is hinged to the other end of the lever L₁ 15, while thelower end thereof is hinged to one end of the fixed rod R₁ 17. The otherend of the fixed rod R₁ 17 is fixed on the mass m₁ 8. The skyhook damperc_(sky) 4 is connected in parallel to the inerter b₂ 3. The skyhookdamper c_(gnd) 7 is connected in parallel to the inerter b₁ 13.

FIG. 11 shows the specific implementation way 2 of the 2DOF passiveskyhook and groundhook damping vibration isolation system. Thedifference between the way 2 and the way 1 is that the lever L₁ 15 andthe lever L₂ 14 are omitted, and a “torsion spring A 19-torsion damper A20” parallel body and a “torsion spring B 21-torsion damper B 22”parallel body are used to replace the “spring k 5-damper c 6” parallelbody and the “spring k_(t) 9-damper c_(t) 10” parallel body in form oftension and compression, respectively. The “torsion spring A 19-torsiondamper A 20” parallel body consists of a torsion spring A 19 and atorsion damper A 20 connected in parallel, and has two common ends, oneof which is fixedly connected to the mass m₁ 8 while the other one ofwhich is hinged to one end of the “spring k₂ 2-inerter b₂ 3” parallelbody. The other end of the “spring k₂ 2-inerter b₂ 3” parallel body ishinged to the mass m₂ 1. The “torsion spring B 21-torsion damper B 22”parallel body consists of a torsion spring B 21 and a torsion damper B22 connected in parallel, and has two common ends, one of which isfixedly connected to the moving foundation 11 while the other one ofwhich is hinged one end of the “spring k₁ 12-inerter b₁ 13” parallelbody. The other end of the “spring k₁ 12-inerter b₁ 13” parallel body ishinged to the mass m₁ 8. The skyhook damper c_(sky) 4 is connected inparallel to the inerter b₂ 3. The skyhook damper c_(gnd) 7 is connectedin parallel to the inerter b₁ 13.

FIG. 12 shows the specific implementation way 3 of the 2DOF passiveskyhook and groundhook damping vibration isolation system. The systemcomprises a mass m₁ 8 and a mass m₂ 1, a skyhook damping pillar 23, agroundhook damping pillar 24 and a moving foundation 11. One end of theskyhook damping pillar 23 is hinged to the mass m₂ 1, while the otherend thereof is hinged to the mass m₁ 8. One end of the groundhookdamping pillar 24 is hinged to the mass m₁ 8, while the other endthereof is hinged to the moving foundation 11.

The skyhook damping pillar 23 comprises a spring k₂ 2, an inerter b₂ 3,a skyhook damper c_(sky) 4, a spring k 5 and a damper c 6. The inerterb₂ 3 is a ballscrew inerter comprising a flywheel chamber A 25, aflywheel A 26, a screw support A 27, a nut A 28, a screw A 29 and astroke chamber A 30. One end of the screw A 29 is a screw portion, whilethe other end thereof is a threaded raceway portion and also has apolished rod portion adjacent to the screw portion. The flywheel A 26 isprovided with a central threaded hole, and is in fitted connection withthe screw portion of the screw A 29. The flywheel chamber A 25 is in acylindrical shape with an open end and a closed end. The open end isfixedly sheathed on the outer circle of the screw support A 27 to ensurethat the flywheel chamber A 25 is coaxial with the screw support A 27. Abearing is mounted within the screw support A 27. The outer ring of thebearing is fitted with an inner hole of the screw support A 27, whilethe inner ring thereof is fitted with the polished rod portion of thescrew A 29, in order to ensure that the position of the screw support A27 is kept unchanged in the axial direction and the radial directionwith respect to the screw A 29 when the screw A 29 rotates with respectto the screw support A 27. The nut A 28 is meshed with the threadedraceway on the screw A 29. The stroke chamber A 30 is in a longcylindrical shape with an open end and a closed end. The open end isfixedly sheathed on the outer circle of the nut A 28 to ensure that thestroke chamber A 30 is coaxial with the nut A 28. The skyhook damperc_(sky) 4 comprises the flywheel chamber A 25, the flywheel A 26 andviscous oil 31. The flywheel chamber is closed and filled with theviscous oil 31 therein. The flywheel A 26 rotates in the viscous oil 31to generate viscous damping under the drive of the screw A 29. Thedamper c 6 comprises a cylinder A 32, a piston A 33 with a damping hole,oil 34 and a piston rod A 35. The cylinder A 32 is connected to thestroke chamber A 30 coaxially and fixedly. The spring k 5 is sheathed onthe outer barrel of the cylinder A 32. One end of the spring k 5 isfixedly connected to one end of the piston rod A 35, while the other endthereof is fixedly connected to the outer barrel of the cylinder A 32.The spring k₂ 2 is sheathed on the outer barrel of the stroke chamber A30. One end of the spring k₂ 2 is fixedly connected to the flywheelchamber A 25, while the other end thereof is fixedly connected to thestroke chamber A 30.

The groundhook damping pillar 24 comprises a spring k₁ 12, an inerter b₁13, a groundhook damper c_(gnd) 7, a spring k_(t) 9 and a damper c_(t)10. The inerter b₁ 13 is a ballscrew inerter comprising a flywheelchamber B 36, a flywheel B 37, a screw support B 38, a nut B 39, a screwB 40 and a stroke chamber B 41. The groundhook damper c_(gnd) 7comprises the flywheel chamber B 36, the flywheel B 37 and viscous oil31. The damper c_(t) 10 comprises a cylinder B 42, a piston B 43 with adamping hole, oil 34 and a piston rod B 44. The groundhook dampingpillar 24 has the same structure as the skyhook damping pillar 23. Theconnection relation of all components of the groundhook damping pillar24 may refer to the skyhook damping pillar 23.

Referring to FIG. 5, the parallel body of the mass m₁ vibration stateconverter 47 and the skyhook damper c_(gnd) 7 in the 2DOF passiveskyhook and groundhook damping vibration isolation system of the presentinvention is omitted, and two ends of the “spring k_(t) 9-damper c_(t)10” parallel body are directly connected in series to the mass m₁ 8 andthe moving foundation 11, respectively, to form a 2DOF passive skyhookdamping vibration isolation system, as shown in FIG. 13.

FIG. 14 shows that there is a big peak on the curve of the displacementtransmissibility of the mass m₂ in the conventional passive vibrationisolation system. The peak is resulted from the resonance of the mass m₂at an inherent frequency, and the frequency is 1.2 Hz. Compared with theconventional passive vibration isolation system, the ideal skyhookdamping vibration isolation system and the passive skyhook dampingvibration isolation system have numerical values at this frequencydecreased by 69.7% and 63.7%, respectively. From the curve in FIG. 14and the above analysis, it can be found that the ideal skyhook vibrationisolation system can suppress the resonance of the mass m₂ completely,and the passive skyhook vibration isolation system can suppress theresonance of the mass m₂ well. The displacement transmissibility of thepassive skyhook vibration isolation system is close to that of the idealskyhook vibration isolation system. The vibration isolation performanceof the two systems is superior to that of the conventional passivevibration isolation system apparently.

Referring to FIG. 5, the parallel body of the mass m₂ vibration stateconverter 45 and the skyhook damper c_(sky) 4 in the 2DOF passiveskyhook and groundhook damping vibration isolation system of the presentinvention is omitted, and two ends of the “spring k 5-damper c 6”parallel body are directly connected in series to the mass m₁ 8 and themass m₂ 1, respectively, to form a 2DOF passive groundhook dampingvibration isolation system, as shown in FIG. 15.

FIG. 16 shows that there is a big peak on the curve of the displacementtransmissibility of the mass m₁ in the conventional passive vibrationisolation system. The peak is resulted from the resonance of the mass m₁at the inherent frequency, and the frequency is 10.2 Hz. Compared withthe conventional passive vibration isolation system, the idealgroundhook damping vibration isolation system and the passive groundhookdamping vibration isolation system have numerical values at thisfrequency decreased by 67.6% and 64.2%, respectively. From the curve inFIG. 16 and the above analysis, it can be found that the idealgroundhook damping vibration isolation system can suppress the resonanceof the mass m₁ completely, and the passive groundhook damping vibrationisolation system can suppress the resonance of the mass m₁ well. Thedisplacement transmissibility of the passive groundhook dampingvibration isolation system is close to that of the ideal groundhookdamping vibration isolation system. The vibration isolation performanceof the two systems is superior to that of the conventional passivevibration isolation system apparently.

Referring to FIG. 5, the “spring k_(t) 9-damper c_(t) 10” parallel body,the parallel body of the mass m₁ vibration state converter 47 and theskyhook damper c_(gnd) 7 and the mass m₁ 8 in the 2DOF passive skyhookand groundhook damping vibration isolation system of the presentinvention are omitted, and the “spring k 5-damper c 6” parallel body isdirectly connected in series to the moving foundation 11, to form anSDOF passive skyhook damping vibration isolation system, as shown inFIG. 17.

The mass m₂ 1 and the mass m₁ 8 may be a vehicle body and vehiclewheels, seats and a vehicle body, a cab and a vehicle body, or seats anda cab.

In addition, the implementation methods and the vibration systemsdisclosed by the present invention are not limited to SDOF and 2DOF, andmay also be expanded to multiple degrees of freedom. The implementationmethods and the vibration systems disclosed by the present invention arealso not limited to the form of translation, and may also be in the formof rotation. The translational elements may be replaced with rotationaland torsional elements.

The foregoing detailed descriptions of the specific implementation waysare provided to illustrate how to preferably implement the presentinvention, and shall not be regarded as any limitation to the scope ofthe present invention. For those skilled in the art, variousmodifications or variations may be made easily to the present inventionaccording to the method given by the present invention to achieve theperformance level of the prevent invention. Therefore, any modificationsand variations shall fall into the scope defined by the claims of thepresent invention.

What is claimed is:
 1. A 2DOF passive skyhook and groundhook dampingvibration isolation system, the system comprising: a spring k-damper cparallel body, a spring k_(t)-damper c_(t) parallel body, a skyhookdamper c_(sky), a groundhook damper c_(gnd), a moving foundation, a massm₁ vibration state converting system, and a mass m₂ vibration stateconverting system; wherein the spring k_(t)-damper c_(t) parallel bodyconsists of a spring k_(t) and a damper c_(t) connected in parallel; themass m₁ vibration state converting system comprises a mass m₁ and a massm₁ vibration state converter, the mass m₁ vibration state converterconsisting of a spring k₁ and an inerter b₁ connected in parallel, themass m₁ vibration state converter being connected in series to andsupporting the mass m₁; the spring k_(t)-damper c_(t) parallel body isconnected in series to the mass m₁ vibration state converter andsupports the whole mass m₁ vibration state converting system via themass m₁ vibration state converter; the moving foundation is connected inseries to and supports the spring k_(t)-damper c_(t) parallel body; thegroundhook damper c_(gnd) is connected in parallel to the mass m₁vibration state converter to form the parallel body of the mass m₁vibration state converter and the groundhook damper c_(gnd); wherein thespring k-damper c parallel body consists of a spring k and a damper cconnected in parallel; the mass m₂ vibration state converting systemcomprises a mass m₂ and a mass m₂ vibration state converter, the mass m₂vibration state converter consisting of a spring k₂ and an inerter b₂connected in parallel, the mass m₂ vibration state converter beingconnected in series to and supporting the mass m₂; the spring k-damper cparallel body is connected in series to the mass m₂ vibration stateconverter, and supports the whole mass m₂ vibration state convertingsystem via the mass m₂ vibration state converter; the mass m₁ isconnected in series to and supports the spring k-damper c parallel body;the skyhook damper c_(sky) is connected in parallel to the mass m₂vibration state converter to form the parallel body of the mass m₂vibration state converter and the skyhook damper c_(sky); wherein in the2DOF passive skyhook and groundhook damping vibration isolation system,the mass of the mass m₂ is m₂, the stiffness of the spring k₂ is k₂, theinerterance of the inerter b₂ is b₂, the damping of the skyhook damperc_(sky) is c_(sky), the stiffness of the spring k is k, the damping ofthe damper c is c; the mass of the mass m₁ is m₁, the stiffness of thespring k₁ is k₁, the inerterance of the inerter b₁ is b₁, the damping ofthe groundhook damper c_(gnd) is c_(gnd), the stiffness of the springk_(t) is k_(t), and the damping of the damper c_(t) is c_(t), wherein k₁and k₂ are selected, as a result k_(t)/3≦k₁≦k_(t) and k/₃≦k₂≦k,$b_{1} = {\frac{k_{1}}{\left( {k_{1} + k} \right)}m_{1}}$ and$b_{2} = {\frac{k_{2}}{k}{m_{2}.}}$
 2. The 2DOF passive skyhook andgroundhook damping vibration isolation system according to claim 1,wherein the mass m₂ comprises a vehicle body, and the mass m₁ comprisesvehicle wheels.
 3. The 2DOF passive skyhook and groundhook dampingvibration isolation system according to claim 1, wherein the mass m₂comprises seats, and the mass m₁ comprises a vehicle body.
 4. The 2DOFpassive skyhook and groundhook damping vibration isolation systemaccording to claim 1, wherein the mass m₂ comprises a cab, and the massm₁ comprises a vehicle body.
 5. The 2DOF passive skyhook and groundhookdamping vibration isolation system according to claim 1, wherein themass m₂ comprises seats, and the mass m₁ comprises a cab.
 6. The 2DOFpassive skyhook and groundhook damping vibration isolation systemaccording to claim 1, wherein the parallel body of the mass m₁ vibrationstate converter and the groundhook damper c_(gnd) and the “springk_(t)-damper c_(t)” parallel body are exchanged in position with eachother.
 7. The 2DOF passive skyhook and groundhook damping vibrationisolation system according to claim 1, wherein the parallel body of themass m₂ vibration state converter and the skyhook damper c_(sky) and thespring k-damper c parallel body are exchanged in position with eachother.
 8. The 2DOF passive skyhook and groundhook damping vibrationisolation system according to claim 1 the inerter b₂ and the inerter b₁are rack and pinion inerters, ballscrew inerters or hydraulic inerters.9. The 2DOF passive skyhook and groundhook damping vibration isolationsystem according to claim 1, further comprising a lever L₁ and a leverL₂, a fixed rod R₁ and a fixed rod R₂, and a slideway, the mass m₂, themass m₁ and the moving foundation being supported on the verticalslideway in a rolling way to slide up and down along the verticalslideway, the fulcrum of the lever L₂ being fixed on the mass m₂, theupper end of the spring k-damper c parallel body being hinged to one endof the lever L₂ while the lower end thereof being hinged to the mass m₁,the upper end of the spring k₂-inerter b₂ parallel body being hinged tothe other end of the lever L₂ while the lower end thereof being hingedto one end of the fixed rod R₂, the other end of the fixed rod R₂ beingfixed on the mass m₂, the fulcrum of the lever L₁ being fixed on themass m₁, the upper end of the spring k_(t)-damper c_(t) parallel bodybeing hinged to one end of the lever L₁ while the lower end thereofbeing hinged to the moving foundation, the upper end of the springk₁-inerter b₁ parallel body being hinged to the other end of the leverL₁ while the lower end thereof being hinged to one end of the fixed rodR₁, the other end of the fixed rod R₁ being fixed on the mass m₁. 10.The 2DOF passive skyhook and groundhook damping vibration isolationsystem according to claim 9, wherein a torsion spring A-torsion damper Aparallel body and a torsion spring B-torsion damper B parallel body areused to replace the “spring k-damper c” parallel body and the springk_(t)-damper c_(t) parallel body; the torsion spring A-torsion damper Aparallel body consists of a torsion spring A and a torsion damper Aconnected in parallel, and has two common ends, one of which beingfixedly connected to the mass m₁ while the other one of which beinghinged to one end of the spring k₂-inerter b₂ parallel body, the otherend of the spring k₂-inerter b₂ parallel body being hinged to the massm₂; the torsion spring B-torsion damper B parallel body consists of atorsion spring B and a torsion damper B connected in parallel, and hastwo common ends, one of which being fixedly connected to the movingfoundation while the other one of which being hinged one end of thespring k₁-inerter b₁ parallel body, the other end of the springk₁-inerter b₁ parallel body being hinged to the mass m₁.
 11. A 2DOFpassive groundhook damping vibration isolation system, wherein theparallel body of the mass m₂ vibration state converter and the skyhookdamper c_(sky) in the 2DOF passive skyhook and groundhook dampingvibration isolation system according to claim 1 is omitted, and two endsof the “spring k-damper c” parallel body are directly connected inseries to the mass m₁ and the mass m₂, respectively.
 12. A 2DOF passiveskyhook damping vibration isolation system, wherein the parallel body ofthe mass m₁ vibration state converter and the skyhook damper c_(gnd) inthe 2DOF passive skyhook and groundhook damping vibration isolationsystem according to claim 1 is omitted, and two ends of the springk_(t)-damper c_(t) parallel body are directly connected in series to themass m₁ and the moving foundation, respectively.
 13. An SDOF passiveskyhook damping vibration isolation system, wherein the springk_(t)-damper c_(t) parallel body, the parallel body of the mass m₁vibration state converter and the skyhook damper c_(gnd) and the mass m₁in the 2DOF passive skyhook and groundhook damping vibration isolationsystem according to claim 1 are omitted, and the spring k-damper cparallel body is directly connected in series to the moving foundation.